contents

1. Introduction?

2．The original Prisoner’s Dilemma scenario in game theory

3. Replication of the payoff matrix using E. coli

3.1 Prisoner coli’s dilemma payoff matrix

3.1.1 Both cooperation leads to low damage

3.1.2 Both defection leads to middle damage

3.1.3 When one is fooled, two types of damage

3.2 Modeling selected a solution for leaky expression problem to satisfy the requirement of the payoff matrix

3.3 Improvementof CmR protein property by addition of ssrA degradation tag

3.4 Succeeded to replicate the payoff matrix through wet lab

4. Prisoner coli decides its option : Cooperate or Defect

4.1 How to decide?

4.2 Decision making coli

5. Iterated game with several strategies

5.1 The four strategies

5.1.1 Random strategy

5.1.2 Always cooperate strategy

5.1.3 Always defect strategy

5.1.4 Tit-for-tat strategy

5.1.4.1 FimE assay: recombinase that inverts fim switch in only one way

6. Dilemma game in general public

7. Reference

1. Introduction

We decided to replay the Prisoner’s Dilemma game, in which one’s profit depend on options of cooperation and defection, by using E. coli. The Prisoner’s Dilemma, a well-known game analyzed in game theory, involves dilemma between cooperation and defection. To pursue his or her own profit, one will choose to cooperate or to defect in the game.
In our E. coli’s version of Prisoner’s Dilemma game involving two prisoner coli, the results of their options define the profit they obtained. Here, profit means the growth of E. coli. Like the prisoners in the game theory, we genetically engineered two E. coli to act as the prisoners, Prisoner A and Prisoner B. The prisoner colis are able to cooperate or to defect in our game. The combinations of their options (cooperation or defection) affect the profit they obtained which equals to their growth. To cooperate, they produce AHL while to defect, they do not produce AHL. Each prisoner coli is designed to produce different type of AHL (C4HSL or 3OC12HSL). The act of producing AHL imposes a metabolic burden on both prisoner coli.

2. The original Prisoner’s Dilemma scenario in game theory

The original Prisoner’s Dilemma scenario involves two members of a criminal gang who were given an option-selection opportunity either to cooperate or to defect according to the payoff matrix (Fig 2.1) in order to pursue for the best profit. This Prisoner’s Dilemma game is a typical example analyzed in game theory. Two members of a criminal gang were arrested by the police. They were separated into two different rooms so that they can’t communicate. In these individual rooms, each prisoner was given an option. Each prisoner was given the opportunity either to cooperate with the other prisoner by remaining silent, or to defect the other criminal by confessing to his crime. Their corresponding punishment is shown in Fig 2.1. This table is called the payoff matrix.

Fig2.1. The payoff matrix in prisoner’s dilemma (punishment = imprisoned years)

From the payoff matrix, one rational option combination, called Nash equilibrium, is both defections. From A’s point of view, if B were to defect, A should choose to defect, comparing 10 years to 5 years of imprisonment. If B were to cooperate, A should choose to cooperate, comparing 2 years to 0 year of imprisonment. In other words, regardless of which option the other decides, each prisoner is punished less by defecting the other. A’s judgement is the same to A, so option of both defections is one rational option combination.

Although both players’ defections result from combination of selfish option selections, the combination of both player’s simultaneous cooperation actually bring more profit to both players than the combination of selfish selections. Apparently, 2 years punishment for both prisoners is not severe than 5 years for both. Thus the combination of both defections is not called Pareto efficiency. This game with such payoff matrix where Nash equilibrium is not Pareto efficiency is called the Prisoner’s Dilemma.